Subgroups — C₅×#26081 #11948801

Order 1280.

690 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3163	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3084	C₂	1	2	yes	maximal
3	C₅×#2912	C₂	1	1	yes	maximal, characteristic
4	C₅×#2090	C₂	1	2	yes	maximal, complemented
5	C₅×#2060	C₂	1	2	yes	maximal, complemented
6	C₅×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1945	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1859	C₂	1	2	yes	maximal
9	C₅×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1815	C₂	1	1	yes	maximal, characteristic
11	C₅×#1764	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₅×#544	C₂²	1	2	yes	—
14	C₅×#520	C₂²	1	2	yes	—
15	C₅×#501	—	2	2	no	—
16	C₅×#499	—	2	1	no	—
17	C₅×#498	—	2	1	no	—
18	C₅×#479	—	2	2	no	—
19	C₅×#478	—	2	2	no	—
20	C₅×#476	—	2	2	no	—
21	C₅×#475	—	2	2	no	—
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₅×#428	—	2	2	no	—
24	C₅×#428	C₂²	1	2	yes	—
25	C₅×#428	C₂²	1	2	yes	—
26	C₅×#428	C₂²	1	2	yes	—
27	C₅×#427	—	2	1	no	—
28	C₅×#427	C₂²	1	1	yes	characteristic
29	C₂×C₅×#106	—	2	1	no	—
30	C₂×C₅×#106	C₂²	1	1	yes	characteristic
31	C₂×C₅×#106	C₂²	1	2	yes	—
32	C₂×C₅×#106	C₂²	1	1	yes	characteristic
33	C₅×#424	C₂²	1	2	yes	—
34	C₂×C₅×#104	C₂²	1	1	yes	characteristic
35	C₅×#417	C₂²	1	2	yes	—
36	C₅×#416	C₂²	1	1	yes	characteristic
37	C₅×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#384	C₂²	1	2	yes	—
40	C₅×#343	C₂²	1	2	yes	—
41	C₅×#343	C₂²	1	2	yes	—
42	C₅×#341	C₂²	1	1	yes	characteristic
43	C₅×#339	C₂²	1	1	yes	characteristic
44	C₅×#339	C₂²	1	2	yes	—
45	#26081	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	C₂³	1	1	yes	characteristic
47	C₅×#131	—	2	2	no	—
48	C₅×#131	Q₈	1	4	yes	complemented
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	C₂³	1	2	yes	—
51	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	—	2	2	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×#125	—	2	2	no	—
59	C₅×#125	—	2	2	no	—
60	C₅×C₂²⋊Q₈	—	4	2	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	4	2	no	—
64	C₅×#117	—	2	2	no	—
65	C₅×#117	C₂³	1	1	yes	characteristic
66	C₅×#117	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	4	2	no	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#108	—	2	2	no	—
73	C₅×#107	—	2	2	no	—
74	C₅×#107	—	2	2	no	—
75	C₅×#107	—	2	2	no	—
76	C₅×#107	D₄	1	2	yes	—
77	C₅×#106	—	2	1	no	—
78	C₅×#106	—	2	1	no	—
79	C₅×#106	—	2	2	no	—
80	C₅×#106	—	2	2	no	—
81	C₅×#106	—	2	1	no	—
82	C₅×#106	—	2	1	no	—
83	C₅×#106	—	2	2	no	—
84	C₅×#106	—	2	2	no	—
85	C₅×#106	—	2	2	no	—
86	C₅×#106	D₄	1	1	yes	characteristic
87	C₅×#106	D₄	1	1	yes	characteristic
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×#104	Q₈	1	4	yes	complemented
91	C₅×#103	—	2	2	no	—
92	C₅×#103	D₄	1	2	yes	—
93	C₅×#102	—	2	2	no	—
94	C₅×#102	D₄	1	2	yes	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	2	no	—
98	#3163	C₂×C₅	1	1	yes	characteristic, complemented
99	#3084	C₂×C₅	1	2	yes	—
100	#2912	C₂×C₅	1	1	yes	characteristic
101	#2090	C₂×C₅	1	2	yes	complemented
102	#2060	C₂×C₅	1	2	yes	complemented
103	#1951	C₂×C₅	1	1	yes	characteristic, complemented
104	#1945	C₂×C₅	1	1	yes	characteristic, complemented
105	#1859	C₂×C₅	1	2	yes	—
106	#1844	C₂×C₅	1	1	yes	characteristic, complemented
107	#1815	C₂×C₅	1	1	yes	characteristic
108	#1764	C₂×C₅	1	1	yes	characteristic
109	C₅×#41	—	2	1	no	—
110	C₅×#41	—	2	1	no	—
111	C₅×#41	C₂×Q₈	1	2	yes	—
112	C₅×#41	C₂×Q₈	1	2	yes	—
113	C₂×C₅×Q₈	—	4	2	no	—
114	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	4	2	no	—
122	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₅×M₁₆	—	2	1	no	—
124	C₅×M₁₆	—	2	1	no	—
125	C₅×M₁₆	—	2	4	no	—
126	C₅×M₁₆	—	2	2	no	—
127	C₅×M₁₆	—	2	2	no	—
128	C₅×M₁₆	C₂×Q₈	1	2	yes	—
129	C₅×M₁₆	C₂×Q₈	1	2	yes	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	4	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
140	C₂×C₅×C₈	#41	1	2	yes	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	—	8	4	no	—
150	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
151	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	4	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	4	2	no	—
160	C₄²×C₅	C₂×Q₈	1	2	yes	—
161	C₂×#131	C₂²×C₅	1	1	yes	characteristic
162	#544	C₂²×C₅	1	2	yes	—
163	#520	C₂²×C₅	1	2	yes	—
164	#501	—	2	2	no	—
165	#499	—	2	1	no	—
166	#498	—	2	1	no	—
167	#479	—	2	2	no	—
168	#478	—	2	2	no	—
169	#476	—	2	2	no	—
170	#475	—	2	2	no	—
171	C₂×#108	C₂²×C₅	1	1	yes	characteristic
172	#428	—	2	2	no	—
173	#428	C₂²×C₅	1	2	yes	—
174	#428	C₂²×C₅	1	2	yes	—
175	#428	C₂²×C₅	1	2	yes	—
176	#427	—	2	1	no	—
177	#427	C₂²×C₅	1	1	yes	characteristic
178	C₂×#106	—	2	1	no	—
179	C₂×#106	C₂²×C₅	1	2	yes	—
180	C₂×#106	C₂²×C₅	1	1	yes	characteristic
181	C₂×#106	C₂²×C₅	1	1	yes	characteristic
182	#424	C₂²×C₅	1	2	yes	—
183	C₂×#104	C₂²×C₅	1	1	yes	characteristic
184	#417	C₂²×C₅	1	2	yes	—
185	#416	C₂²×C₅	1	1	yes	characteristic
186	#405	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	#384	C₂²×C₅	1	2	yes	—
189	#343	C₂²×C₅	1	2	yes	—
190	#343	C₂²×C₅	1	2	yes	—
191	#341	C₂²×C₅	1	1	yes	characteristic
192	#339	C₂²×C₅	1	1	yes	characteristic
193	#339	C₂²×C₅	1	2	yes	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
196	C₅×Q₈	—	2	1	no	—
197	C₅×Q₈	—	16	2	no	—
198	C₅×Q₈	C₄⋊Q₈	1	2	yes	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	2	1	no	—
202	C₅×D₄	C₄⋊Q₈	1	2	yes	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	8	2	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	16	2	no	—
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	—	4	2	no	—
226	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
227	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
228	C₂×#41	C₂³×C₅	1	1	yes	characteristic
229	#131	—	2	2	no	—
230	#131	C₅×Q₈	1	4	yes	complemented
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	C₂³×C₅	1	2	yes	—
233	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
234	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	#125	—	2	2	no	—
241	#125	—	2	2	no	—
242	C₂²⋊Q₈	—	4	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	4	2	no	—
246	#117	—	2	2	no	—
247	#117	C₂³×C₅	1	2	yes	—
248	#117	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	4	2	no	—
251	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#108	—	2	2	no	—
255	#107	—	2	2	no	—
256	#107	—	2	2	no	—
257	#107	—	2	2	no	—
258	#107	C₅×D₄	1	2	yes	—
259	#106	—	2	1	no	—
260	#106	—	2	1	no	—
261	#106	—	2	2	no	—
262	#106	—	2	2	no	—
263	#106	—	2	1	no	—
264	#106	—	2	1	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	—	2	2	no	—
268	#106	C₅×D₄	1	1	yes	characteristic
269	#106	C₅×D₄	1	1	yes	characteristic
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#104	C₅×Q₈	1	4	yes	complemented
273	#103	—	2	2	no	—
274	#103	C₅×D₄	1	2	yes	—
275	#102	—	2	2	no	—
276	#102	C₅×D₄	1	2	yes	—
277	#97	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	2	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	#544	1	1	yes	characteristic
284	C₂²×C₅	D₄²	1	1	yes	characteristic
285	C₂²×C₅	#554	1	1	yes	characteristic
286	C₄×C₅	—	2	4	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	—	8	2	no	—
293	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
294	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
295	C₄×C₅	#547	1	1	yes	characteristic
296	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
297	#41	—	2	1	no	—
298	#41	—	2	1	no	—
299	#41	C₂×C₅×Q₈	1	2	yes	—
300	#41	C₂×C₅×Q₈	1	2	yes	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
311	M₁₆	—	2	1	no	—
312	M₁₆	—	2	1	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	C₂×C₅×Q₈	1	2	yes	—
317	M₁₆	C₂×C₅×Q₈	1	2	yes	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
325	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
328	C₂×C₈	C₅×#41	1	2	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	8	4	no	—
338	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
339	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
340	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	4	2	no	—
348	C₄²	C₂×C₅×Q₈	1	2	yes	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	2	1	no	—
351	C₂×C₅	—	4	2	no	—
352	C₂×C₅	#2440	1	1	yes	characteristic
353	C₂×C₅	#3291	1	2	yes	—
354	C₂³	—	2	1	no	—
355	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
356	Q₈	—	2	1	no	—
357	Q₈	—	16	2	no	—
358	Q₈	C₅×C₄⋊Q₈	1	2	yes	—
359	D₄	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	C₅×C₄⋊Q₈	1	2	yes	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	16	2	no	—
376	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	2	no	—
386	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
387	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
388	C₅	#26081	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₅×#544	1	1	yes	characteristic
393	C₂²	C₅×D₄²	1	1	yes	characteristic
394	C₂²	C₅×#554	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	2	no	—
402	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
403	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
404	C₄	C₅×#547	1	1	yes	characteristic
405	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	4	2	no	—
409	C₂	C₅×#2440	1	1	yes	characteristic
410	C₂	C₅×#3291	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#3163	C₂	semidirect
4. C₅×#2090	C₂	semidirect
5. C₅×#2060	C₂	semidirect
6. C₅×#1951	C₂	semidirect
7. C₅×#1945	C₂	semidirect
9. C₅×#1844	C₂	semidirect
45. #26081	C₅	direct (N × H)
48. C₅×#131	Q₈	semidirect
90. C₅×#104	Q₈	semidirect
98. #3163	C₂×C₅	semidirect
101. #2090	C₂×C₅	semidirect
102. #2060	C₂×C₅	semidirect
103. #1951	C₂×C₅	semidirect
104. #1945	C₂×C₅	semidirect
106. #1844	C₂×C₅	semidirect
230. #131	C₅×Q₈	semidirect
272. #104	C₅×Q₈	semidirect
388. C₅	#26081	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3163	2
C₅×#3084	2
C₅×#2912	2
C₅×#2090	2
C₅×#2060	2
C₅×#1951	2
C₅×#1945	2
C₅×#1859	2
C₅×#1844	2
C₅×#1815	2
C₅×#1764	2
#26081	5

Subgroups — C5×#26081 #11948801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26081 #11948801